System (REF ) is often known as CH2 or CH(2,1) system, see [1]}, and it reduces to the CH equation (REF ) whenever \(\rho =0\) . It is interesting to note that the CH2 system and the CH equation were both born in the context of integrable systems in [2]}, [3]} and [4]}, respectively, and latter shown in [5]} and [6]} their physical relevance as shallow water models. Their similarities, however, are not restricted to their birth since the CH2 system shares several properties with the CH equation, such as:
